Speaking after he met leaders of all Croatia's parliamentary parties, Prime Minister Zoran Milanović said parliament would be asked to approve the decision to leave the talks on Wednesday.
"Unfortunately, the (arbitration) process has been contaminated and Croatia cannot stay in it. We have to cancel the arbitration agreement," Milanović told a news conference, adding that the parties had agreed unanimously to withdraw.
The court of arbitration has three international judges plus one each from Croatia and Slovenia and is meant to be independent of national governments. Last Wednesday, however, Zagreb-based daily Večernji List published excerpts from a leaked tape in which Slovenian judge Jernej Sekolec discusses confidential details of the case, the probable outcomes and strategy, with Simona Drenik, who represents Slovenia's Foreign Ministry before the court.
Both resigned on Thursday without giving any statements. Slovenia is now planning to appoint a new judge to replace Sekolec, in the hope that arbitration will continue.
"I believe that Croatia cannot leave this process in line with the rules," Slovenian Prime Minister Miro Cerar said on Monday. "Things should calm down and the process should continue so that the (arbitration) court can end its work."
Milanović said there will be no hostility between Croatia and Slovenia, adding: "It is an embarrassing situation for everyone ... There are no precedents in the history of border arbitrations so no one knows what will happen."
While there is no deadline for the panel to report after starting work in 2011, Croatian and Slovenian media reports have suggested it is due reach a decision this year.
The dispute over land and sea borders in the northern Adriatic Piran Bay, where Slovenia wants direct access to international waters, prompted Ljubljana to block talks in 2008 on Croatian membership of the European Union. The two republics agreed to international border arbitration, a deal that allowed Croatia to join the EU in 2013, nine years after Slovenia.